Abstract:
Based on the Wang–Landau algorithm, the Monte Carlo method was used to study the magnetic structures of the ground state and the thermodynamic properties of the two-dimensional Potts model with the number of spin states $q$ = 4 on a triangular lattice, taking into account the exchange interactions of the first $J_1$ and second $J_2$ nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the range -2.0 $\le J_2\le$ 0.0. The magnetic structures of the ground state are constructed in the interval considered. An energy analysis of the magnetic structures of the ground state has been carried out. A phase diagram of the dependence of the critical temperature on the value of $J_2$ is constructed. It is shown that taking into account the interactions of the second nearest neighbors leads to the appearance of frustrations and violation of the magnetic ordering.
Keywords:frustrations, magnetic structures, Monte Carlo method, Potts model.